An Improved Extra-Gradient Method for Minimizing a Sum of p-norms--A Variational Inequality Approach

Authors:
Xiao-Ming Yuan;Li Zhou
Affiliations:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong;Department of Mathematics, Nanjing University, Nanjing, China 210093
Venue:
Computational Optimization and Applications
Year:
2006

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Abstract

This paper presents a variational inequality (VI) approach to the problem of minimizing a sum of p-norms. First the original problem is reformulated as an equivalent linear VI. Then an improved extra-gradient method is presented to solve the linear VI. Applications to the problem of p-norm Steiner Minimum Trees (SMT) shows that the proposed method is effective. Comparison with the general extra-gradient method is also provided to show the improvements of the new method.